Question

An element occurs in bcc structure. Its density is 8.0 g cm⁻³. If the cell edge is 250 pm, the atomic mass of the element is ______.

Options

• 26.4 g mol⁻¹

• 37.6 g mol⁻¹

• 54.5 g mol⁻¹

• 86.1 g mol⁻¹

Answer 1

An element occurs in bcc structure. Its density is 8.0 g cm⁻³. If the cell edge is 250 pm, the atomic mass of the element is 37.6 g mol⁻¹.

Explanation:

Given: The structure is Body-Centred Cubic (BCC), the number of atoms per unit cell is Z = 2.

Density (ρ) = 8.0 g/cm³

Edge length (a) = 250 pm = 2.5 × 10⁻⁸ cm

Avogadro’s number (N_A) = 6.022 × 10²³ mol⁻¹

To find: atomic mass (M) = ?

`rho = (Z xx M)/(a^3 xx N_A)`

⇒ `M = (rho xx a^3 xx N_A)/Z`

`M = (8.0 xx (2.5 xx 10^-8)^3 xx (6.022 xx 10^23))/2`

`M = (8.0 xx (15.625 xx 10^-24) xx (6.022 xx 10^23))/2`

`M = (8.0 xx 94.09 xx 10^-1)/2`

`M = 752.72/2`

M = 376.36 × 10⁻¹

M = 37.6 g mol⁻¹